The system of linear equations
`x+lambday -z=0`
`lambdax -y-z=0`
`x+y-lambdaz=0`
has a non-trivial solution for

The set of all values of lambda for which the system of linear equations x - 2y - 2z = lambdax x + 2y + z = lambday -x -y = lambdaz has a non-trivial solution

The set of all values of lambda for which the system of linear equations: x-2y-2z=lambdax , x+2y+z=lambday and -x-y=lambdaz has a non-trivial solution: (a) is an empty sheet (b) is a singleton (c) contains more than two elements (d) contains exactly two elements

The number of real values of for which the system of linear equations 2x+4y- lambdaz =0 , 4x+lambday +2z=0 , lambdax + 2y+2z=0 has infinitely many solutions , is :

The number of distinct real values of lamda for which the system of linear equations x + y + z = lamda x , x + y + z = lamday, x + y + z + lamda z has non - trival solution.

The value(s) of lambda for which the system of equations (1-lambda)x+3y-4z=0 x-(3+lambda)y + 5z=0 3x+y-lambdaz=0 possesses non-trivial solutions .

x+ky-z=0 , 3x-ky-z=0 and x-3y+z=0 has non-zero solution for k=

The greatest value of for which the system of linear equations x-cy-cz=0 cx-y+cz=0 cx+cy-z=0 Has a non-trivial solution, is 1/k . The value of k is _________.

Statement 1: If the system of equation lambdax+(b-a)y+(c-a)z=0,(a-b)x+lambday+(c-b)z=0,a n d(a-c)x+(b-c)y+lambdaz=0 has a non trivial solution, then the value of lambda is 0. Statement 2: the value of skew symmetric matrix of order 3 is Zero.

Determine the values of lambda for which the following system of equations : lambdax+3y-z=1 , x+2y+z=2 , -lambdax+y+2z=-1 has non-trival solutions.

Show that the homogenous system of equations x - 2y + z = 0, x + y - z = 0, 3 x + 6y - 5z = 0 has a non-trivial solution. Also find the solution